Calculus Examples

$lim_{x \to 1} \frac{12 x^{2} - 5 x}{x}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $1$ .

$\frac{lim_{x \to 1} 12 x^{2} - 5 x}{lim_{x \to 1} x}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$\frac{lim_{x \to 1} 12 x^{2} - lim_{x \to 1} 5 x}{lim_{x \to 1} x}$

Step 3

Move the term $12$ outside of the limit because it is constant with respect to $x$ .

$\frac{12 lim_{x \to 1} x^{2} - lim_{x \to 1} 5 x}{lim_{x \to 1} x}$

Step 4

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

$\frac{12 {(lim_{x \to 1} x)}^{2} - lim_{x \to 1} 5 x}{lim_{x \to 1} x}$

Step 5

Move the term $5$ outside of the limit because it is constant with respect to $x$ .

$\frac{12 {(lim_{x \to 1} x)}^{2} - 5 lim_{x \to 1} x}{lim_{x \to 1} x}$

Step 6

Evaluate the limits by plugging in $1$ for all occurrences of $x$ .

Tap for more steps...

Step 6.1

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\frac{12 \cdot 1^{2} - 5 lim_{x \to 1} x}{lim_{x \to 1} x}$

Step 6.2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\frac{12 \cdot 1^{2} - 5 \cdot 1}{lim_{x \to 1} x}$

Step 6.3

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\frac{12 \cdot 1^{2} - 5 \cdot 1}{1}$

Step 7

Simplify the answer.

Tap for more steps...

Step 7.1

Divide $12 \cdot 1^{2} - 5 \cdot 1$ by $1$ .

$12 \cdot 1^{2} - 5 \cdot 1$

Step 7.2

Simplify each term.

Tap for more steps...

Step 7.2.1

One to any power is one.

$12 \cdot 1 - 5 \cdot 1$

Step 7.2.2

Multiply $12$ by $1$ .

$12 - 5 \cdot 1$

Step 7.2.3

Multiply $- 5$ by $1$ .

$12 - 5$

Step 7.3

Subtract $5$ from $12$ .

$7$